Transmission not shifting properly?

Have to put pedal almost to floor to get into reverse and then it's quite a jerk. Doesn't want to shift right, was able to get up to 40 MPH to bring it home. Have had to let it warm up for the last year before driving as it didn't shift into higher gear until 6 or 7 minutes of driving. New fluid and everything a year ago. My mechanic said transmission is bad. Listed for sale on marketplace and have had a few people say it could be in limp mode for a different reason and to check with you guys. I'm not interested in throwing a bunch of money at it, it was my winter car and I've bought a different one but a guy responding on marketplace advised checking with you before selling it for parts. I don't feel that it would jerk like that into reverse if it was just in limp mode, but figured I would ask. Thanks!